A Note on Finite Nilpotent Groups

被引：0
|
作者：
Werner, Nicholas J. [1 ]
机构：
[1] State Univ New York Coll Old Westbury, Dept Math Comp & Informat Sci, Old Westbury, NY 11568 USA
来源：
AMERICAN MATHEMATICAL MONTHLY | 2024年 / 131卷 / 09期
关键词：
20D15;
D O I：
10.1080/00029890.2024.2379751
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is well known that if G is a group and H is a normal subgroup of G of finite index k, then x(k )is an element of H for every x is an element of G. We examine finite groups G with the property that x(k )is an element of H for every subgroup H of G, where k is the index of H in G. We prove that a finite group G satisfies this property if and only if G is nilpotent.
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页码：803 / 805
页数：3
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